Entropy of the Kerr–Sen black hole

We study the entropy of Kerr–Sen black hole of heterotic string theory beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law of thermodynamics, we derive the corrections to the entropy of the black hole. The leading (logarithmic) and non-leading corrections to the area law are obtained.     

Anomaly analysis of Hawking radiation from Kaluza–Klein black hole with squashed horizon

Considering gravitational and gauge anomalies at the horizon, a new method to derive Hawking radiation from black holes has been developed by Wilczek et al. In this paper, we apply this method to non-rotating and rotating Kaluza–Klein black holes with squashed horizon, respectively. For the rotating case, we found that, after dimensional reduction, an effective U(1) gauge field is generated by an angular isometry. The results show that the gauge current and energy-momentum tensor fluxes are exactly equivalent to Hawking radiation from the event horizon.     

Kaluza–Klein reductions and AdS/Ricci-flat correspondence

The AdS/Ricci-flat (AdS/RF) correspondence is a map between families of asymptotically locally AdS solutions on a torus and families of asymptotically flat spacetimes on a sphere. The aim of this work is to perturbatively extend this map to general AdS and asymptotically flat solutions. A prime application for such map would be the development of holography for Minkowski spacetime. In this paper we perform a Kaluza–Klein (KK) reduction of AdS on a torus and of Minkowski on a sphere, keeping all massive KK modes. Such computation is interesting on its own, as there are relatively few examples of such explicit KK reductions in the literature. We perform both KK reductions in parallel to illustrate their similarity. In particular, we show how to construct gauge invariant variables, find the field equations they satisfy, and construct a corresponding effective action. We further diagonalize all equations and find their general solution in closed form. Surprisingly, in the limit of large dimension of the compact manifolds (torus and sphere), the AdS/RF correspondence maps individual KK modes from one side to the other. In a sequel of this paper we will discuss how the AdS/RF maps acts on general linear perturbations.     

Hawking temperature of Kerr–Newman–AdS black hole from tunneling

Using the null-geodesic tunneling method of Parikh and Wilczek, we derive the Hawking temperature of a general four-dimensional rotating black hole. In order to eliminate the motion of ? degree of freedom of a tunneling particle, we have chosen a reference system that is co-rotating with the black hole horizon. Then we give the explicit result for the Hawking temperature of the Kerr–Newman–AdS black hole from the tunneling approach.     

Entropy and topology of the Kerr—de Sitter black hole

By using the path integral method of Gibbons and Hawking, the entropy of the Kerr-de Sitter black hole is investigated under the microcanonical ensemble. We find that the entropy is one eighth the sum of the products of the Euler number of its cosmological horizon and event horizon with their respective areas. It is shown that the origin of the entropy of the black hole is related to the topology of its instanton.     

Charged black holes on Kaluza–Klein bubbles

We construct exact solutions of the Einstein–Maxwell field equations in five dimensions, which describe general configurations of charged and static black holes sitting on a Kaluza–Klein bubble. More specifically we discuss the configurations describing two black holes sitting on a Kaluza–Klein bubble and also the general charged static black Saturn balanced by a Kaluza–Klein bubble. A straightforward extension of the solution-generating technique leads to a new solution describing the charged static black Saturn on the Taub-bolt instanton. We compute the conserved charges and investigate some of the thermodynamic properties of these systems.     

Covariant anomalies and Hawking radiation from Kaluza–Klein AdS black holes

In this paper, Hawking radiation is studied from four-dimensional (4D) Kaluza–Klein (KK) AdS black holes via the method of anomaly cancellation. The KK-AdS black hole considered is a non-extremal charged rotating solution in the theory of 4D gauged supergravity. Its Hawking fluxes of electric charge, angular momentum and energy momentum tensor are derived here. Our results support the common view that Hawking radiation is the quantum effect arising at the event horizon.     

Hawking radiation of Kerr–Newman–de Sitter black hole

We extend the classical Damour–Ruffini method and discuss Hawking radiation in Kerr–Newman–de Sitter (KNdS) black hole. Under the condition that the total energy, angular momentum and charge of spacetime are conserved, taking the reaction of the radiation of the particle to the spacetime and the relation between the black hole event horizon and the cosmological horizon into consideration, we derive the black hole radiation spectrum. The radiation spectrum is no longer a pure thermal one. It is related to the change of the Bekenstein–Hawking entropy corresponding the black hole event horizon and the cosmological horizon. It is consistent with the underlying unitary theory.     

Cosmological Kaluza–Klein branes in black brane spacetimes

We discuss the cosmological evolution of a brane in the D(>6)$D(>6)$-dimensional black brane spacetime in the context of the Kaluza–Klein (KK) braneworld scheme, i.e., to consider KK compactification on the brane. The bulk spacetime is composed of two copies of a patch of D  -dimensional black three-brane solution. The near-horizon geometry is given by AdS₅×S(D−5)${\mathit{AdS}}_5\times S^{(D-5)}$ while in the asymptotic infinity the spacetime approaches D-dimensional Minkowski. We consider the brane motion from the near-horizon region toward the spatial infinity, which induces cosmology on the brane. As is expected, in the early times, namely when the brane is located in the near-horizon region, the effective cosmology on the brane coincides with that in the second Randall–Sundrum (RS II) model. Then, the brane cosmology starts to deviate from the RS type one since the dynamics of KK compactified dimensions becomes significant. We find that the brane Universe cannot reach the asymptotic infinity, irrespectively of the components of matter on the brane.     

Hawking radiation of Dirac particles from Kerr–AdS black hole in five dimensions

By constructing a set of appropriate matrices γμ${\gamma }^{\mu }$ for general covariant Dirac equation, we further extend fermion tunneling method to 5-dimensional Kerr–AdS black hole, and show that the expected Hawking temperature is recovered.     

Wiggly strings of radial configuration in Kerr–Newman black hole

Previously we have investigated the cosmic wiggly strings in (3 + 1)-dimensional Schwarzschild, Reissner–Nordström and Kerr black holes. As an extension the solutions in (3 + 1)-dimensional axially symmetric charged rotating black hole are investigated. The solutions for the wiggly string exhibit open strings lying in the radial direction in the equatorial plane outside the horizon.     

Tunnelling effect of the non-stationary Kerr black hole

Extending Parikh and Wilczek＇s work to the non-stationary black hole, we study the Hawking radiation of the non-stationary Kerr black hole by the Hamilto-Jacobi method. The result shows that the radiation spectrum is not purely thermal and the tunnelling probability is related to the change of Bekenstein Hawking entropy, which gives a correction to the Hawking thermal radiation of the black hole.     

Einstein–Rosen solutions from Kaluza–Klein theory

From a time-dependent boost-rotational symmetric vacuum solution of the Einstein Equations in five dimensions, through the Kaluza–Klein reduction the corresponding Einstein–Maxwell-dilaton solutions are obtained. The four dimensional counterpart turns out to be generalized Einstein–Rosen spacetimes representing unpolarized gravitational waves traveling in an inhomogeneous cosmology. Restricting the parameters we are able to obtain different 4D time-dependent solutions equipped with scalar and electromagnetic fields.     

Effects of thermal fluctuations on the Kerr–Newman–NUT–AdS black hole

This paper is devoted to studying the impact of thermal fluctuations on thermodynamics of rotating as well as charged anti-de Sitter black holes with the Newman–Unti–Tamburino(NUT)parameter. To this end, we derive the analytic expression of thermodynamic variables, namely the Hawking temperature, volume, angular velocity, and entropy within the limits of extended phase space. These variables meet the first law of thermodynamics as well as the Smarr relation in the presence of new NUT charge. To analyze the effects of quantum fluctuations, we derive the exact expression of corrected entropy, which yields modification in other thermodynamical equations of state. The local stability and phase transition of the considered black hole are also examined through specific heat. It is found that the NUT parameter increases the stability of small black holes, while the logarithmic corrections induce instability in the system.     

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.     

Energy of the Kerr–Newman-AdS black hole by using approximate Lie symmetries

Using Lie approximate symmetry methods for differential equations second-order approximate symmetries of the geodesic equations for the Kerr–Newman-AdS (KN-AdS) spacetime are investigated. For this purpose the KN-AdS metric is considered as a second perturbation of the AdS metric. A rescaling of the arc length parameter for consistency of the trivial second-order approximate symmetries of the geodesic equations indicates that the energy in the KN-AdS spacetime has to be rescaled. There is an extra contribution to the energy of the KN-AdS spacetime due to the cosmological constant. This energy expression is compared with that for the Kerr–Newman (KN) spacetime.     

Kerr–Newman black hole thermodynamical state space: blockwise coordinates

A coordinate system that blockwise-simplifies the Kerr–Newman black hole’s thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner–Nordström and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr–Newman case’s 3 by 3 thermodynamical state space metric.